draft-ietf-rmt-bb-fec-rs-03.txt   draft-ietf-rmt-bb-fec-rs-04.txt 
Reliable Multicast Transport J. Lacan Reliable Multicast Transport J. Lacan
Internet-Draft ENSICA/LAAS-CNRS Internet-Draft ISAE
Intended status: Experimental V. Roca Intended status: Standards Track V. Roca
Expires: November 8, 2007 INRIA Expires: April 12, 2008 INRIA
J. Peltotalo J. Peltotalo
S. Peltotalo S. Peltotalo
Tampere University of Technology Tampere University of Technology
May 7, 2007 October 10, 2007
Reed-Solomon Forward Error Correction (FEC) Schemes Reed-Solomon Forward Error Correction (FEC) Schemes
draft-ietf-rmt-bb-fec-rs-03.txt draft-ietf-rmt-bb-fec-rs-04.txt
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Copyright Notice Copyright Notice
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Abstract Abstract
This document describes a Fully-Specified FEC Scheme for the Reed- This document describes a Fully-Specified Forward Error Correction
Solomon forward error correction codes over GF(2^^m), with m in (FEC) Scheme for the Reed-Solomon FEC codes over GF(2^^m), with m in
{2..16}, and its application to the reliable delivery of data objects {2..16}, and its application to the reliable delivery of data objects
on the packet erasure channel. on the packet erasure channel.
This document also describes a Fully-Specified FEC Scheme for the This document also describes a Fully-Specified FEC Scheme for the
special case of Reed-Solomon codes over GF(2^^8) when there is no special case of Reed-Solomon codes over GF(2^^8) when there is no
encoding symbol group. encoding symbol group.
Finally, in the context of the Under-Specified Small Block Systematic Finally, in the context of the Under-Specified Small Block Systematic
FEC Scheme (FEC Encoding ID 129), this document assigns an FEC FEC Scheme (FEC Encoding ID 129), this document assigns an FEC
Instance ID to the special case of Reed-Solomon codes over GF(2^^8). Instance ID to the special case of Reed-Solomon codes over GF(2^^8).
Reed-Solomon codes belong to the class of Maximum Distance Separable Reed-Solomon codes belong to the class of Maximum Distance Separable
(MDS) codes, i.e. they enable a receiver to recover the k source (MDS) codes, i.e., they enable a receiver to recover the k source
symbols from any set of k received symbols. The schemes described symbols from any set of k received symbols. The schemes described
here are compatible with the implementation from Luigi Rizzo. here are compatible with the implementation from Luigi Rizzo.
Table of Contents Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4
2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 5 2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 5
3. Definitions Notations and Abbreviations . . . . . . . . . . . 6 3. Definitions Notations and Abbreviations . . . . . . . . . . . 6
3.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 6 3.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 6
3.2. Notations . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2. Notations . . . . . . . . . . . . . . . . . . . . . . . . 6
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8. Reed-Solomon Codes Specification for the Erasure Channel . . . 17 8. Reed-Solomon Codes Specification for the Erasure Channel . . . 17
8.1. Finite Field . . . . . . . . . . . . . . . . . . . . . . . 17 8.1. Finite Field . . . . . . . . . . . . . . . . . . . . . . . 17
8.2. Reed-Solomon Encoding Algorithm . . . . . . . . . . . . . 18 8.2. Reed-Solomon Encoding Algorithm . . . . . . . . . . . . . 18
8.2.1. Encoding Principles . . . . . . . . . . . . . . . . . 18 8.2.1. Encoding Principles . . . . . . . . . . . . . . . . . 18
8.2.2. Encoding Complexity . . . . . . . . . . . . . . . . . 19 8.2.2. Encoding Complexity . . . . . . . . . . . . . . . . . 19
8.3. Reed-Solomon Decoding Algorithm . . . . . . . . . . . . . 19 8.3. Reed-Solomon Decoding Algorithm . . . . . . . . . . . . . 19
8.3.1. Decoding Principles . . . . . . . . . . . . . . . . . 19 8.3.1. Decoding Principles . . . . . . . . . . . . . . . . . 19
8.3.2. Decoding Complexity . . . . . . . . . . . . . . . . . 20 8.3.2. Decoding Complexity . . . . . . . . . . . . . . . . . 20
8.4. Implementation for the Packet Erasure Channel . . . . . . 20 8.4. Implementation for the Packet Erasure Channel . . . . . . 20
9. Security Considerations . . . . . . . . . . . . . . . . . . . 23 9. Security Considerations . . . . . . . . . . . . . . . . . . . 23
10. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 24 9.1. Problem Statement . . . . . . . . . . . . . . . . . . . . 23
11. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 25 9.2. Attacks Against the Data Flow . . . . . . . . . . . . . . 23
12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 26 9.3. Attacks against the FEC parameters . . . . . . . . . . . . 25
12.1. Normative References . . . . . . . . . . . . . . . . . . . 26 10. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 26
12.2. Informative References . . . . . . . . . . . . . . . . . . 26 11. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 27
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 28 12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Intellectual Property and Copyright Statements . . . . . . . . . . 29 12.1. Normative References . . . . . . . . . . . . . . . . . . . 28
12.2. Informative References . . . . . . . . . . . . . . . . . . 28
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 30
Intellectual Property and Copyright Statements . . . . . . . . . . 31
1. Introduction 1. Introduction
The use of Forward Error Correction (FEC) codes is a classical The use of Forward Error Correction (FEC) codes is a classical
solution to improve the reliability of multicast and broadcast solution to improve the reliability of multicast and broadcast
transmissions. The [2] document describes a general framework to use transmissions. The [2] document describes a general framework to use
FEC in Content Delivery Protocols (CDP). The companion document [4] FEC in Content Delivery Protocols (CDP). The companion document [4]
describes some applications of FEC codes for content delivery. describes some applications of FEC codes for content delivery.
Recent FEC schemes like [9] and [10] proposed erasure codes based on Recent FEC schemes like [9] and [8] proposed erasure codes based on
sparse graphs/matrices. These codes are efficient in terms of sparse graphs/matrices. These codes are efficient in terms of
processing but not optimal in terms of correction capabilities when processing but not optimal in terms of correction capabilities when
dealing with "small" objects. dealing with "small" objects.
The FEC scheme described in this document belongs to the class of The FEC scheme described in this document belongs to the class of
Maximum Distance Separable codes that are optimal in terms of erasure Maximum Distance Separable codes that are optimal in terms of erasure
correction capability. In others words, it enables a receiver to correction capability. In others words, it enables a receiver to
recover the k source symbols from any set of exactly k encoding recover the k source symbols from any set of exactly k encoding
symbols. Even if the encoding/decoding complexity is larger than symbols. Even if the encoding/decoding complexity is larger than
that of [9] or [10], this family of codes is very useful. that of [9] or [8], this family of codes is very useful.
Many applications dealing with content transmission or content Many applications dealing with content transmission or content
storage already rely on packet-based Reed-Solomon codes. In storage already rely on packet-based Reed-Solomon codes. In
particular, many of them use the Reed-Solomon codec of Luigi Rizzo particular, many of them use the Reed-Solomon codec of Luigi Rizzo
[7]. The goal of the present document to specify an implementation [5]. The goal of the present document to specify an implementation
of Reed-Solomon codes that is compatible with this codec. of Reed-Solomon codes that is compatible with this codec.
The present document: The present document:
o introduces the Fully-Specified FEC Scheme with FEC Encoding ID 2 o introduces the Fully-Specified FEC Scheme with FEC Encoding ID 2
that specifies the use of Reed-Solomon codes over GF(2^^m), with m that specifies the use of Reed-Solomon codes over GF(2^^m), with m
in {2..16}, in {2..16},
o introduces the Fully-Specified FEC Scheme with FEC Encoding ID 5 o introduces the Fully-Specified FEC Scheme with FEC Encoding ID 5
that focuses on the special case of Reed-Solomon codes over that focuses on the special case of Reed-Solomon codes over
GF(2^^8) and no encoding symbol group (i.e. exactly one symbol per GF(2^^8) and no encoding symbol group (i.e., exactly one symbol
packet), and per packet), and
o in the context of the Under-Specified Small Block Systematic FEC o in the context of the Under-Specified Small Block Systematic FEC
Scheme (FEC Encoding ID 129) [3], assigns the FEC Instance ID 0 to Scheme (FEC Encoding ID 129) [3], assigns the FEC Instance ID 0 to
the special case of Reed-Solomon codes over GF(2^^8) and no the special case of Reed-Solomon codes over GF(2^^8) and no
encoding symbol group. encoding symbol group.
2. Terminology 2. Terminology
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
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This document uses the following notations: This document uses the following notations:
L denotes the object transfer length in bytes. L denotes the object transfer length in bytes.
k denotes the number of source symbols in a source block. k denotes the number of source symbols in a source block.
n_r denotes the number of repair symbols generated for a source n_r denotes the number of repair symbols generated for a source
block. block.
n denotes the encoding block length, i.e. the number of encoding n denotes the encoding block length, i.e., the number of encoding
symbols generated for a source block. Therefore: n = k + n_r. symbols generated for a source block. Therefore: n = k + n_r.
max_n denotes the maximum number of encoding symbols generated for max_n denotes the maximum number of encoding symbols generated for
any source block. any source block.
B denotes the maximum source block length in symbols, i.e. the B denotes the maximum source block length in symbols, i.e., the
maximum number of source symbols per source block. maximum number of source symbols per source block.
N denotes the number of source blocks into which the object shall N denotes the number of source blocks into which the object shall
be partitioned. be partitioned.
E denotes the encoding symbol length in bytes. E denotes the encoding symbol length in bytes.
S denotes the symbol size in units of m-bit elements. When m = 8, S denotes the symbol size in units of m-bit elements. When m = 8,
then S and E are equal. then S and E are equal.
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In this document, m belongs to {2..16}. In this document, m belongs to {2..16}.
q defines the number of elements in the finite field. We have: q q defines the number of elements in the finite field. We have: q
= 2^^m in this specification. = 2^^m in this specification.
G denotes the number of encoding symbols per group, i.e. the G denotes the number of encoding symbols per group, i.e. the
number of symbols sent in the same packet. number of symbols sent in the same packet.
GM denotes the Generator Matrix of a Reed-Solomon code. GM denotes the Generator Matrix of a Reed-Solomon code.
rate denotes the "code rate", i.e. the k/n ratio. rate denotes the "code rate", i.e., the k/n ratio.
a^^b denotes a raised to the power b. a^^b denotes a raised to the power b.
a^^-1 denotes the inverse of a. a^^-1 denotes the inverse of a.
I_k denotes the k*k identity matrix. I_k denotes the k*k identity matrix.
3.3. Abbreviations 3.3. Abbreviations
This document uses the following abbreviations: This document uses the following abbreviations:
ESI stands for Encoding Symbol ID. ESI stands for Encoding Symbol ID.
FEC OTI stands for FEC Object Transmission Information. FEC OTI stands for FEC Object Transmission Information.
RS stands for Reed-Solomon. RS stands for Reed-Solomon.
MDS stands for Maximum Distance Separable code. MDS stands for Maximum Distance Separable code.
GF(q) denotes a finite field (A.K.A. Galois Field) with q GF(q) denotes a finite field (also known as Galois Field) with q
elements. We assume that q = 2^^m in this document. elements. We assume that q = 2^^m in this document.
4. Formats and Codes with FEC Encoding ID 2 4. Formats and Codes with FEC Encoding ID 2
This section introduces the formats and codes associated to the This section introduces the formats and codes associated to the
Fully-Specified FEC Scheme with FEC Encoding ID 2 that specifies the Fully-Specified FEC Scheme with FEC Encoding ID 2 that specifies the
use of Reed-Solomon codes over GF(2^^m). use of Reed-Solomon codes over GF(2^^m).
4.1. FEC Payload ID 4.1. FEC Payload ID
The FEC Payload ID is composed of the Source Block Number and the The FEC Payload ID is composed of the Source Block Number and the
Encoding Symbol ID. The length of these two fields depends on the Encoding Symbol ID. The length of these two fields depends on the
parameter m (which is transmitted in the FEC OTI) as follows: parameter m (which is transmitted in the FEC OTI) as follows:
o The Source Block Number (field of size 32-m bits) identifies from o The Source Block Number (field of size 32-m bits) identifies from
which source block of the object the encoding symbol(s) in the which source block of the object the encoding symbol(s) in the
payload is(are) generated. There are a maximum of 2^^(32-m) payload is(are) generated. There is a maximum of 2^^(32-m) blocks
blocks per object. per object.
o The Encoding Symbol ID (field of size m bits) identifies which o The Encoding Symbol ID (field of size m bits) identifies which
specific encoding symbol(s) generated from the source block specific encoding symbol(s) generated from the source block
is(are) carried in the packet payload. There are a maximum of is(are) carried in the packet payload. There is a maximum of 2^^m
2^^m encoding symbols per block. The first k values (0 to k - 1) encoding symbols per block. The first k values (0 to k - 1)
identify source symbols, the remaining n-k values identify repair identify source symbols, the remaining n-k values identify repair
symbols. symbols.
There MUST be exactly one FEC Payload ID per source or repair packet. There MUST be exactly one FEC Payload ID per source or repair packet.
In case of an Encoding Symbol Group, when multiple encoding symbols In case of an Encoding Symbol Group, when multiple encoding symbols
are sent in the same packet, the FEC Payload ID refers to the first are sent in the same packet, the FEC Payload ID refers to the first
symbol of the packet. The other symbols can be deduced from the ESI symbol of the packet. The other symbols can be deduced from the ESI
of the first symbol by incrementing sequentially the ESI. of the first symbol by incrementing sequentially the ESI.
The format of the FEC Payload ID for m = 8 and m = 16 is illustrated
in Figure 1 and Figure 2 respectively.
0 1 2 3 0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Number (32-8=24 bits) | Enc. Symb. ID | | Source Block Number (32-8=24 bits) | Enc. Symb. ID |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 1: FEC Payload ID encoding format for m = 8 (default) Figure 1: FEC Payload ID encoding format for m = 8 (default)
0 1 2 3 0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
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| Source Block Number (32-8=24 bits) | Enc. Symb. ID | | Source Block Number (32-8=24 bits) | Enc. Symb. ID |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 1: FEC Payload ID encoding format for m = 8 (default) Figure 1: FEC Payload ID encoding format for m = 8 (default)
0 1 2 3 0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Src Block Nb (32-16=16 bits) | Enc. Symbol ID (m=16 bits) | | Src Block Nb (32-16=16 bits) | Enc. Symbol ID (m=16 bits) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 2: FEC Payload ID encoding format for m = 16 Figure 2: FEC Payload ID encoding format for m = 16
The format of the FEC Payload ID for m = 8 and m = 16 is illustrated
in Figure 1 and Figure 2 respectively.
4.2. FEC Object Transmission Information 4.2. FEC Object Transmission Information
4.2.1. Mandatory Elements 4.2.1. Mandatory Elements
o FEC Encoding ID: the Fully-Specified FEC Scheme described in this o FEC Encoding ID: the Fully-Specified FEC Scheme described in this
section uses FEC Encoding ID 2. section uses FEC Encoding ID 2.
4.2.2. Common Elements 4.2.2. Common Elements
The following elements MUST be defined with the present FEC scheme: The following elements MUST be defined with the present FEC scheme:
o Transfer-Length (L): a non-negative integer indicating the length o Transfer-Length (L): a non-negative integer indicating the length
of the object in bytes. There are some restrictions on the of the object in bytes. There are some restrictions on the
maximum Transfer-Length that can be supported: maximum Transfer-Length that can be supported:
max_transfer_length = 2^^(32-m) * B * E max_transfer_length = 2^^(32-m) * B * E
For instance, for m = 8, for B = 2^^8 - 1 (because the codec For instance, for m = 8, for B = 2^^8 - 1 (because the codec
operates on a finite field with 2^^8 elements) and if E = 1024 operates on a finite field with 2^^8 elements) and if E = 1024
bytes, then the maximum transfer length is approximately equal to bytes, then the maximum transfer length is approximately equal to
2^^42 bytes (i.e. 4 Tera Bytes). Similarly, for m = 16, for B = 2^^42 bytes (i.e., 4 Tera Bytes). Similarly, for m = 16, for B =
2^^16 - 1 and if E = 1024 bytes, then the maximum transfer length 2^^16 - 1 and if E = 1024 bytes, then the maximum transfer length
is also approximately equal to 2^^42 bytes. For larger objects, is also approximately equal to 2^^42 bytes. For larger objects,
another FEC scheme, with a larger Source Block Number field in the another FEC scheme, with a larger Source Block Number field in the
FEC Payload ID, could be defined. Another solution consists in FEC Payload ID, could be defined. Another solution consists in
fragmenting large objects into smaller objects, each of them fragmenting large objects into smaller objects, each of them
complying with the above limits. complying with the above limits.
o Encoding-Symbol-Length (E): a non-negative integer indicating the o Encoding-Symbol-Length (E): a non-negative integer indicating the
length of each encoding symbol in bytes. length of each encoding symbol in bytes.
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The following element MUST be defined with the present FEC Scheme. The following element MUST be defined with the present FEC Scheme.
It contains two distinct pieces of information: It contains two distinct pieces of information:
o G: a non-negative integer indicating the number of encoding o G: a non-negative integer indicating the number of encoding
symbols per group used for the object. The default value is 1, symbols per group used for the object. The default value is 1,
meaning that each packet contains exactly one symbol. When no G meaning that each packet contains exactly one symbol. When no G
parameter is communicated to the decoder, then this latter MUST parameter is communicated to the decoder, then this latter MUST
assume that G = 1. assume that G = 1.
o Finite Field parameter, m: The m parameter is the length of the o m: The m parameter is the length of the finite field elements, in
finite field elements, in bits. It also characterizes the number bits. It also characterizes the number of elements in the finite
of elements in the finite field: q = 2^^m elements. The default field: q = 2^^m elements. The default value is m = 8. When no
value is m = 8. When no finite field size parameter is finite field size parameter is communicated to the decoder, then
communicated to the decoder, then this latter MUST assume that m = this latter MUST assume that m = 8.
8.
4.2.4. Encoding Format 4.2.4. Encoding Format
This section shows the two possible encoding formats of the above FEC This section shows the two possible encoding formats of the above FEC
OTI. The present document does not specify when one encoding format OTI. The present document does not specify when one encoding format
or the other should be used. or the other should be used.
4.2.4.1. Using the General EXT_FTI Format 4.2.4.1. Using the General EXT_FTI Format
The FEC OTI binary format is the following, when the EXT_FTI The FEC OTI binary format is the following, when the EXT_FTI
mechanism is used (e.g. within the ALC [11] or NORM [12] protocols). mechanism is used (e.g., within the ALC [10] or NORM [11] protocols).
0 1 2 3 0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| HET = 64 | HEL = 4 | | | HET = 64 | HEL = 4 | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +
| Transfer-Length (L) | | Transfer-Length (L) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| m | G | Encoding Symbol Length (E) | | m | G | Encoding Symbol Length (E) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Max Source Block Length (B) | Max Nb Enc. Symbols (max_n) | | Max Source Block Length (B) | Max Nb Enc. Symbols (max_n) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 3: EXT_FTI Header Format Figure 3: EXT_FTI Header Format
4.2.4.2. Using the FDT Instance (FLUTE specific) 4.2.4.2. Using the FDT Instance (FLUTE specific)
When it is desired that the FEC OTI be carried in the FDT Instance of When it is desired that the FEC OTI be carried in the FDT (File
a FLUTE session [13], the following XML attributes must be described Delivery Table) Instance of a FLUTE session [12], the following XML
for the associated object: attributes must be described for the associated object:
o FEC-OTI-FEC-Encoding-ID o FEC-OTI-FEC-Encoding-ID
o FEC-OTI-Transfer-Length (L) o FEC-OTI-Transfer-Length (L)
o FEC-OTI-Encoding-Symbol-Length (E) o FEC-OTI-Encoding-Symbol-Length (E)
o FEC-OTI-Maximum-Source-Block-Length (B) o FEC-OTI-Maximum-Source-Block-Length (B)
o FEC-OTI-Max-Number-of-Encoding-Symbols (max_n) o FEC-OTI-Max-Number-of-Encoding-Symbols (max_n)
skipping to change at page 12, line 19 skipping to change at page 12, line 19
special case of Reed-Solomon codes over GF(2^^8) and no encoding special case of Reed-Solomon codes over GF(2^^8) and no encoding
symbol group. symbol group.
5.1. FEC Payload ID 5.1. FEC Payload ID
The FEC Payload ID is composed of the Source Block Number and the The FEC Payload ID is composed of the Source Block Number and the
Encoding Symbol ID: Encoding Symbol ID:
o The Source Block Number (24 bit field) identifies from which o The Source Block Number (24 bit field) identifies from which
source block of the object the encoding symbol in the payload is source block of the object the encoding symbol in the payload is
generated. There are a maximum of 2^^24 blocks per object. generated. There is a maximum of 2^^24 blocks per object.
o The Encoding Symbol ID (8 bit field) identifies which specific o The Encoding Symbol ID (8 bit field) identifies which specific
encoding symbol generated from the source block is carried in the encoding symbol generated from the source block is carried in the
packet payload. There are a maximum of 2^^8 encoding symbols per packet payload. There is a maximum of 2^^8 encoding symbols per
block. The first k values (0 to k - 1) identify source symbols, block. The first k values (0 to k - 1) identify source symbols,
the remaining n-k values identify repair symbols. the remaining n-k values identify repair symbols.
There MUST be exactly one FEC Payload ID per source or repair packet. There MUST be exactly one FEC Payload ID per source or repair packet.
This FEC Payload ID refer to the one and only symbol of the packet. This FEC Payload ID refer to the one and only symbol of the packet.
0 1 2 3 0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Number (24 bits) | Enc. Symb. ID | | Source Block Number (24 bits) | Enc. Symb. ID |
skipping to change at page 13, line 18 skipping to change at page 13, line 18
5.2.4. Encoding Format 5.2.4. Encoding Format
This section shows the two possible encoding formats of the above FEC This section shows the two possible encoding formats of the above FEC
OTI. The present document does not specify when one encoding format OTI. The present document does not specify when one encoding format
or the other should be used. or the other should be used.
5.2.4.1. Using the General EXT_FTI Format 5.2.4.1. Using the General EXT_FTI Format
The FEC OTI binary format is the following, when the EXT_FTI The FEC OTI binary format is the following, when the EXT_FTI
mechanism is used (e.g. within the ALC [11] or NORM [12] protocols). mechanism is used (e.g., within the ALC [10] or NORM [11] protocols).
0 1 2 3 0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| HET = 64 | HEL = 3 | | | HET = 64 | HEL = 3 | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +
| Transfer-Length (L) | | Transfer-Length (L) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Symbol Length (E) | MaxBlkLen (B) | max_n | | Encoding Symbol Length (E) | MaxBlkLen (B) | max_n |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 6: EXT_FTI Header Format with FEC Encoding ID 5 Figure 6: EXT_FTI Header Format with FEC Encoding ID 5
5.2.4.2. Using the FDT Instance (FLUTE specific) 5.2.4.2. Using the FDT Instance (FLUTE specific)
When it is desired that the FEC OTI be carried in the FDT Instance of When it is desired that the FEC OTI be carried in the FDT Instance of
a FLUTE session [13], the following XML attributes must be described a FLUTE session [12], the following XML attributes must be described
for the associated object: for the associated object:
o FEC-OTI-FEC-Encoding-ID o FEC-OTI-FEC-Encoding-ID
o FEC-OTI-Transfer-Length (L) o FEC-OTI-Transfer-Length (L)
o FEC-OTI-Encoding-Symbol-Length (E) o FEC-OTI-Encoding-Symbol-Length (E)
o FEC-OTI-Maximum-Source-Block-Length (B) o FEC-OTI-Maximum-Source-Block-Length (B)
skipping to change at page 14, line 17 skipping to change at page 14, line 17
This section defines procedures that are common to FEC Encoding IDs 2 This section defines procedures that are common to FEC Encoding IDs 2
and 5. In case of FEC Encoding ID 5, m = 8 and G = 1. Note that the and 5. In case of FEC Encoding ID 5, m = 8 and G = 1. Note that the
block partitioning algorithm is defined in [2]. block partitioning algorithm is defined in [2].
6.1. Determining the Maximum Source Block Length (B) 6.1. Determining the Maximum Source Block Length (B)
The finite field size parameter, m, defines the number of non zero The finite field size parameter, m, defines the number of non zero
elements in this field which is equal to: q - 1 = 2^^m - 1. Note elements in this field which is equal to: q - 1 = 2^^m - 1. Note
that q - 1 is also the theoretical maximum number of encoding symbols that q - 1 is also the theoretical maximum number of encoding symbols
that can be produced for a source block. For instance, when m = 8 that can be produced for a source block. For instance, when m = 8
(default): (default) there is a maximum of 2^^8 - 1 = 255 encoding symbols.
max1_B = 2^^8 - 1 = 255 Given the target FEC code rate (e.g., provided by the user when
starting a FLUTE sending application), the sender calculates:
max1_B = floor((2^^m - 1) * rate)
This max1_B value leaves enough room for the sender to produce the
desired number of parity symbols.
Additionally, a codec MAY impose other limitations on the maximum Additionally, a codec MAY impose other limitations on the maximum
block size. Yet it is not expected that such limits exist when using block size. Yet it is not expected that such limits exist when using
the default m = 8 value. This decision MUST be clarified at the default m = 8 value. This decision MUST be clarified at
implementation time, when the target use case is known. This results implementation time, when the target use case is known. This results
in a max2_B limitation. in a max2_B limitation.
Then, B is given by: Then, B is given by:
B = min(max1_B, max2_B) B = min(max1_B, max2_B)
skipping to change at page 14, line 49 skipping to change at page 15, line 8
AT A SENDER: AT A SENDER:
Input: Input:
B: Maximum source block length, for any source block. Section 6.1 B: Maximum source block length, for any source block. Section 6.1
explains how to determine its value. explains how to determine its value.
k: Current source block length. This parameter is given by the k: Current source block length. This parameter is given by the
block partitioning algorithm. block partitioning algorithm.
rate: FEC code rate, which is given by the user (e.g. when rate: FEC code rate, which is given by the user (e.g., when
starting a FLUTE sending application). It is expressed as a starting a FLUTE sending application). It is expressed as a
floating point value. floating point value.
Output: Output:
max_n: Maximum number of encoding symbols generated for any source max_n: Maximum number of encoding symbols generated for any source
block block.
n: Number of encoding symbols generated for this source block n: Number of encoding symbols generated for this source block.
Algorithm: Algorithm:
max_n = floor(B / rate); max_n = ceil(B / rate);
if (max_n > 2^^m - 1) then return an error ("invalid code rate"); if (max_n > 2^^m - 1) then return an error ("invalid code rate");
n = floor(k * max_n / B); n = floor(k * max_n / B);
AT A RECEIVER: AT A RECEIVER:
Input: Input:
B: Extracted from the received FEC OTI B: Extracted from the received FEC OTI.
max_n: Extracted from the received FEC OTI max_n: Extracted from the received FEC OTI.
k: Given by the block partitioning algorithm k: Given by the block partitioning algorithm.
Output: Output:
n n
Algorithm: Algorithm:
n = floor(k * max_n / B); n = floor(k * max_n / B);
Note that a Reed-Solomon decoder does not need to know the n value. Note that a Reed-Solomon decoder does not need to know the n value.
skipping to change at page 16, line 16 skipping to change at page 16, line 16
Solomon Codes over GF(2^^8) Solomon Codes over GF(2^^8)
In the context of the Under-Specified Small Block Systematic FEC In the context of the Under-Specified Small Block Systematic FEC
Scheme (FEC Encoding ID 129) [3], this document assigns the FEC Scheme (FEC Encoding ID 129) [3], this document assigns the FEC
Instance ID 0 to the special case of Reed-Solomon codes over GF(2^^8) Instance ID 0 to the special case of Reed-Solomon codes over GF(2^^8)
and no encoding symbol group. and no encoding symbol group.
The FEC Instance ID 0 uses the Formats and Codes specified in [3]. The FEC Instance ID 0 uses the Formats and Codes specified in [3].
The FEC Scheme with FEC Instance ID 0 MAY use the algorithm defined The FEC Scheme with FEC Instance ID 0 MAY use the algorithm defined
in Section 9.1. of [3] to partition the file into source blocks. in Section 9.1. of [2] to partition the file into source blocks.
This FEC Scheme MAY also use another algorithm. For instance the CDP This FEC Scheme MAY also use another algorithm. For instance the CDP
sender may change the length of each source block dynamically, sender may change the length of each source block dynamically,
depending on some external criteria (e.g. to adjust the FEC coding depending on some external criteria (e.g., to adjust the FEC coding
rate to the current loss rate experienced by NORM receivers) and rate to the current loss rate experienced by NORM receivers) and
inform the CDP receivers of the current block length by means of the inform the CDP receivers of the current block length by means of the
EXT_FTI mechanism. This choice is out of the scope of the current EXT_FTI mechanism. This choice is out of the scope of the current
document. document.
8. Reed-Solomon Codes Specification for the Erasure Channel 8. Reed-Solomon Codes Specification for the Erasure Channel
Reed-Solomon (RS) codes are linear block codes. They also belong to Reed-Solomon (RS) codes are linear block codes. They also belong to
the class of MDS codes. A [n,k]-RS code encodes a sequence of k the class of MDS codes. A [n,k]-RS code encodes a sequence of k
source elements defined over a finite field GF(q) into a sequence of source elements defined over a finite field GF(q) into a sequence of
skipping to change at page 17, line 25 skipping to change at page 17, line 25
m-bit elements, and Section 8.4 the use of [n,k]-RS codes when m-bit elements, and Section 8.4 the use of [n,k]-RS codes when
applied to symbols composed of several m-bit elements, which is the applied to symbols composed of several m-bit elements, which is the
target of this specification. target of this specification.
8.1. Finite Field 8.1. Finite Field
A finite field GF(q) is defined as a finite set of q elements which A finite field GF(q) is defined as a finite set of q elements which
has a structure of field. It contains necessarily q = p^^m elements, has a structure of field. It contains necessarily q = p^^m elements,
where p is a prime number. With packet erasure channels, p is always where p is a prime number. With packet erasure channels, p is always
set to 2. The elements of the field GF(2^^m) can be represented by set to 2. The elements of the field GF(2^^m) can be represented by
polynomials with binary coefficients (i.e. over GF(2)) of degree polynomials with binary coefficients (i.e., over GF(2)) of degree
lower or equal than m-1. The polynomials can be associated to binary lower or equal than m-1. The polynomials can be associated to binary
vectors of length m. For example, the vector (11001) represents the vectors of length m. For example, the vector (11001) represents the
polynomial 1 + x + x^^4. This representation is often called polynomial 1 + x + x^^4. This representation is often called
polynomial representation. The addition between two elements is polynomial representation. The addition between two elements is
defined as the addition of binary polynomials in GF(2) and the defined as the addition of binary polynomials in GF(2) and the
multiplication is the multiplication modulo a given irreducible multiplication is the multiplication modulo a given irreducible
polynomial over GF(2) of degree m with coefficients in GF(2). Note polynomial over GF(2) of degree m with coefficients in GF(2). Note
that all the roots of this polynomial are in GF(2^^m) but not in that all the roots of this polynomial are in GF(2^^m) but not in
GF(2). GF(2).
skipping to change at page 19, line 25 skipping to change at page 19, line 25
Note that, in practice, the [n,k]-RS code can be shortened to a Note that, in practice, the [n,k]-RS code can be shortened to a
[n',k]-RS code, where k <= n' < n, by considering the sub-matrix [n',k]-RS code, where k <= n' < n, by considering the sub-matrix
formed by the n' first columns of GM. formed by the n' first columns of GM.
8.2.2. Encoding Complexity 8.2.2. Encoding Complexity
Encoding can be performed by first pre-computing GM and by Encoding can be performed by first pre-computing GM and by
multiplying the source vector (k elements) by GM (k rows and n multiplying the source vector (k elements) by GM (k rows and n
columns). The complexity of the pre-computation of the generator columns). The complexity of the pre-computation of the generator
matrix can be estimated as the complexity of the multiplication of matrix can be estimated as the complexity of the multiplication of
the inverse of a Vandermonde matrix by n-k vectors (i.e. the last n-k the inverse of a Vandermonde matrix by n-k vectors (i.e., the last
columns of V_{k,n}). Since the complexity of the inverse of a k*k- n-k columns of V_{k,n}). Since the complexity of the inverse of a
Vandermonde matrix by a vector is O(k * log^^2(k)), the generator k*k-Vandermonde matrix by a vector is O(k * log^^2(k)), the generator
matrix can be computed in 0((n-k)* k * log^^2(k)) operations. When matrix can be computed in 0((n-k)* k * log^^2(k)) operations. When
the generator matrix is pre-computed, the encoding needs k operations the generator matrix is pre-computed, the encoding needs k operations
per repair element (vector-matrix multiplication). per repair element (vector-matrix multiplication).
Encoding can also be performed by first computing the product s * Encoding can also be performed by first computing the product s *
V_{k,k}^^-1 and then by multiplying the result with V_{k,n}. The V_{k,k}^^-1 and then by multiplying the result with V_{k,n}. The
multiplication by the inverse of a square Vandermonde matrix is known multiplication by the inverse of a square Vandermonde matrix is known
as the interpolation problem and its complexity is O(k * log^^2 (k)). as the interpolation problem and its complexity is O(k * log^^2 (k)).
The multiplication by a Vandermonde matrix, known as the multipoint The multiplication by a Vandermonde matrix, known as the multipoint
evaluation problem, requires O((n-k) * log(k)) by using Fast Fourier evaluation problem, requires O((n-k) * log(k)) by using Fast Fourier
Transform, as explained in [14]. The total complexity of this Transform, as explained in [7]. The total complexity of this
encoding algorithm is then O((k/(n-k)) * log^^2(k) + log(k)) encoding algorithm is then O((k/(n-k)) * log^^2(k) + log(k))
operations per repair element. operations per repair element.
8.3. Reed-Solomon Decoding Algorithm 8.3. Reed-Solomon Decoding Algorithm
8.3.1. Decoding Principles 8.3.1. Decoding Principles
The Reed-Solomon decoding algorithm for the erasure channel allows The Reed-Solomon decoding algorithm for the erasure channel allows
the recovery of the k source elements from any set of k received the recovery of the k source elements from any set of k received
elements. It is based on the fundamental property of the generator elements. It is based on the fundamental property of the generator
matrix which is such that any k*k-submatrix is invertible (see [8]). matrix which is such that any k*k-submatrix is invertible (see [6]).
The first step of the decoding consists in extracting the k*k The first step of the decoding consists in extracting the k*k
submatrix of the generator matrix obtained by considering the columns submatrix of the generator matrix obtained by considering the columns
corresponding to the received elements. Indeed, since any encoding corresponding to the received elements. Indeed, since any encoding
element is obtained by multiplying the source vector by one column of element is obtained by multiplying the source vector by one column of
the generator matrix, the received vector of k encoding elements can the generator matrix, the received vector of k encoding elements can
be considered as the result of the multiplication of the source be considered as the result of the multiplication of the source
vector by a k*k submatrix of the generator matrix. Since this vector by a k*k submatrix of the generator matrix. Since this
submatrix is invertible, the second step of the algorithm is to submatrix is invertible, the second step of the algorithm is to
invert this matrix and to multiply the received vector by the invert this matrix and to multiply the received vector by the
obtained matrix to recover the source vector. obtained matrix to recover the source vector.
skipping to change at page 20, line 45 skipping to change at page 20, line 45
known. The following specification describes the use of Reed-Solomon known. The following specification describes the use of Reed-Solomon
codes for generating redundant symbols from the k source symbols and codes for generating redundant symbols from the k source symbols and
for recovering the source symbols from any set of k received symbols. for recovering the source symbols from any set of k received symbols.
The k source symbols of a source block are assumed to be composed of The k source symbols of a source block are assumed to be composed of
S m-bit elements. Each m-bit element corresponds to an element of S m-bit elements. Each m-bit element corresponds to an element of
the finite field GF(2^^m) through the polynomial representation the finite field GF(2^^m) through the polynomial representation
(Section 8.1). If some of the source symbols contain less than S (Section 8.1). If some of the source symbols contain less than S
elements, they MUST be virtually padded with zero elements (it can be elements, they MUST be virtually padded with zero elements (it can be
the case for the last symbol of the last block of the object). the case for the last symbol of the last block of the object).
However, this padding need not be actually sent with the data to the However, this padding does not need to be actually sent with the data
receivers. to the receivers.
The encoding process produces n encoding symbols of size S m-bit The encoding process produces n encoding symbols of size S m-bit
elements, of which k are source symbols (this is a systematic code) elements, of which k are source symbols (this is a systematic code)
and n-k are repair symbols (Figure 7). The m-bit elements of the and n-k are repair symbols (Figure 7). The m-bit elements of the
repair symbols are calculated using the corresponding m-bit elements repair symbols are calculated using the corresponding m-bit elements
of the source symbol set. A logical j-th source vector, comprised of of the source symbol set. A logical j-th source vector, comprised of
the j-th elements from the set of source symbols, is used to the j-th elements from the set of source symbols, is used to
calculate a j-th encoding vector. This j-th encoding vector then calculate a j-th encoding vector. This j-th encoding vector then
provides the j-th elements for the set encoding symbols calculated provides the j-th elements for the set encoding symbols calculated
for the block. As a systematic code, the first k encoding symbols for the block. As a systematic code, the first k encoding symbols
are the same as the k source symbols and the last n-k repair symbols are the same as the k source symbols and the last n-k repair symbols
are the result of the Reed Solomon encoding. are the result of the Reed-Solomon encoding.
Input: k source symbols Input: k source symbols
0 j S-1 0 j S-1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |X| | source symbol 0 | |X| | source symbol 0
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |X| | source symbol 1 | |X| | source symbol 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
. . . . . .
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |X| | source symbol k-1 | |X| | source symbol k-1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
* *
+----------------+ +--------------------+
| generator | | generator matrix |
| matrix |
| GM | | GM |
| (k x n) | | (k x n) |
+----------------+ +--------------------+
| |
V V
Output: n encoding symbols (source + repair) Output: n encoding symbols (source + repair)
0 j S-1 0 j S-1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |X| | enc. symbol 0 | |X| | enc. symbol 0
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |X| | enc. symbol 1 | |X| | enc. symbol 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
. . . . . .
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |Y| | enc. symbol n-1 | |Y| | enc. symbol n-1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 7: Packet encoding scheme
Figure 7: Packet encoding scheme
An asset of this scheme is that the loss of some encoding symbols An asset of this scheme is that the loss of some encoding symbols
produces the same erasure pattern for each of the S encoding vectors. produces the same erasure pattern for each of the S encoding vectors.
It follows that the matrix inversion must be done only once and will It follows that the matrix inversion must be done only once and will
be used by all the S encoding vectors. For large S, this matrix be used by all the S encoding vectors. For large S, this matrix
inversion cost becomes negligible in front of the S matrix-vector inversion cost becomes negligible in front of the S matrix-vector
multiplications. multiplications.
Another asset is that the n-k repair symbols can be produced on Another asset is that the n-k repair symbols can be produced on
demand. For instance, a sender can start by producing a limited demand. For instance, a sender can start by producing a limited
number of repair symbols and later on, depending on the observed number of repair symbols and later on, depending on the observed
erasures on the channel, decide to produce additional repair symbols, erasures on the channel, decide to produce additional repair symbols,
up to the n-k upper limit. Indeed, to produce the repair symbol e_j, up to the n-k upper limit. Indeed, to produce the repair symbol e_j,
where k <= j < n, it is sufficient to multiply the S source vectors where k <= j < n, it is sufficient to multiply the S source vectors
with column j of GM. with column j of GM.
9. Security Considerations 9. Security Considerations
Data delivery can be subject to denial-of-service attacks by 9.1. Problem Statement
attackers which send corrupted packets that are accepted as
legitimate by receivers. This is particularly a concern for
multicast delivery because a corrupted packet may be injected into
the session close to the root of the multicast tree, in which case
the corrupted packet will arrive at many receivers. This is
particularly a concern for the FEC building block because the use of
even one corrupted packet containing encoding data may result in the
decoding of an object that is completely corrupted and unusable. It
is thus RECOMMENDED that source authentication and integrity checking
are applied to decoded objects before delivering objects to an
application. For example, a SHA-1 hash [5] of an object may be
appended before transmission, and the SHA-1 hash is computed and
checked after the object is decoded but before it is delivered to an
application. Source authentication SHOULD be provided, for example
by including a digital signature verifiable by the receiver computed
on top of the hash value. It is also RECOMMENDED that a packet
authentication protocol such as TESLA [6] be used to detect and
discard corrupted packets upon arrival. Furthermore, it is
RECOMMENDED that Reverse Path Forwarding checks be enabled in all
network routers and switches along the path from the sender to
receivers to limit the possibility of a bad agent successfully
injecting a corrupted packet into the multicast tree data path.
Another security concern is that some FEC information may be obtained A content delivery system is potentially subject to many attacks:
by receivers out-of-band in a session description, and if the session some of them target the network (e.g., to compromise the routing
description is forged or corrupted then the receivers will not use infrastructure, by compromising the congestion control component),
the correct protocol for decoding content from received packets. To others target the Content Delivery Protocol (CDP) (e.g., to
avoid these problems, it is RECOMMENDED that measures be taken to compromise its normal behavior), and finally some attacks target the
prevent receivers from accepting incorrect session descriptions, content itself. Since this document focuses on a FEC building block
e.g., by using source authentication to ensure that receivers only independently of any particular CDP (even if ALC and NORM are two
accept legitimate session descriptions from authorized senders. natural candidates), this section only discusses the additional
threats that an arbitrary CDP may be exposed to when using this
building block.
More specifically, several kinds of attacks exist:
o those that are meant to give access to a confidential content
(e.g., in case of a non-free content),
o those that try to corrupt the object being transmitted (e.g., to
inject malicious code within an object, or to prevent a receiver
from using an object),
o and those that try to compromise the receiver's behavior (e.g., by
making the decoding of an object computationally expensive).
These attacks can be launched either against the data flow itself
(e.g. by sending forged symbols) or against the FEC parameters that
are sent either in-band (e.g., in an EXT_FTI or FDT Instance) or out-
of-band (e.g., in a session description).
9.2. Attacks Against the Data Flow
First of all, let us consider the attacks against the data flow.
Access control is typically provided by means of encryption. This
encryption can be done over the whole object (e.g., by the content
provider, before the FEC encoding process), or be done on a packet
per packet basis (e.g., when IPSec/ESP is used [14]). If access
control is a concern, it is RECOMMENDED that one of these solutions
be used. Even if we mention these attacks here, they are not related
nor facilitated by the use of FEC.
Protection against corruptions (forged packets) is achieved by means
of a content integrity verification/sender authentication scheme.
This service can be provided at the object level, but in that case a
receiver has no way to identify which symbol(s) is(are) corrupted if
the object is detected as corrupted. This service can also be
provided at the packet level, and after having removed all forged
packets, the object can be recovered if the number of symbols
remaining is sufficient. Several techniques can provide this source
authentication/content integrity service:
o at the object level, the object MAY be digitally signed (with
public key cryptography) (e.g., using RSASSA-PKCS1-v1_5 [13]).
This signature enables a receiver to check the object, once this
latter has been fully decoded. Even if digital signatures are
computationally expensive, this calculation occurs only once per
object, which is usually acceptable;
o at the packet level, each packet can be digitally signed. A major
limitation is the high computational and transmission overheads
that this solution incurs (unless ECC is used, but ECC is
protected by IPR). To avoid this problem, the signature may span
a set of symbols in order to amortize the signature calculation,
but if a single symbol is missing, the integrity of the whole set
cannot be checked;
o at the packet level, a Group Message Authentication Code (MAC)
[15] (e.g., using HMAC-SHA-1 with a secret key shared by all the
group members, senders and receivers) scheme can be used. This
technique creates a cryptographically secured (thanks to the
secret key) digest of a packet that is sent along with the packet.
The Group MAC scheme does not incur prohibitive processing load
nor transmission overhead, but it has a major limitation: it only
provides a group authentication/integrity service since all group
members share the same secret group key, which means that each
member can send a forged packet. It is therefore restricted to
situations where group members are fully trusted (or in
association with another technique as a pre-check);
o at the packet level, TESLA [16] is a very attractive and efficient
solution that is robust to losses, provides a true authentication/
integrity service, and does not incur any prohibitive processing
load or transmission overhead.
It is up to the developer, who knows the security requirements of the
target use-case, to define which solution is the most appropriate.
Nonetheless, it is RECOMMENDED that at least one of these techniques
be used.
Techniques relying on public key cryptography (digital signatures and
TESLA during the bootstrap process) require that public keys be
securely associated to the entities. This can be achieved by a
Public Key Infrastructure (PKI), or by a PGP Web of Trust, or by pre-
distributing the public keys of each group member. It is up to the
developer, who knows the features of the target use-case, to define
which solution to use.
Techniques relying on symmetric key cryptography (group MAC) require
that a secret key be shared by all group members. This can be
achieved by means of a group key management protocol, or simply by
pre-distributing the secret key (but this manual solution has many
limitations). Here also, it is up to the developer to define which
solution to use, taking into account the target use-case features.
9.3. Attacks against the FEC parameters
Let us now consider attacks against the FEC parameters (or FEC OTI).
The FEC OTI can either be sent in-band (i.e., in an EXT_FTI or in an
FDT Instance containing FEC OTI for the object) or out-of-band (e.g.,
in a session description). Attacks on these FEC parameters can
prevent the decoding of the associated object: for instance modifying
the B parameter will lead to a different block partitioning at a
receiver thereby compromising decoding; or setting the m parameter to
16 instead of 8 with FEC Encoding ID 2 will increase the processing
load while compromising decoding.
It is therefore RECOMMENDED that security measures be taken to
guarantee the FEC OTI integrity. To that purpose, the packets
carrying the FEC parameters sent in-band (i.e., in an EXT_FTI header
extension or in an FDT Instance) may be protected by one of the per-
packet techniques described above: TESLA, digital signature, or a
group MAC. Alternatively, when FEC OTI is contained in an FDT
Instance, this object may be digitally signed. Finally, when FEC OTI
is sent out-of-band for instance in a session description, this
latter may be protected by a digital signature.
The same considerations concerning the key management aspects apply
here also.
10. IANA Considerations 10. IANA Considerations
Values of FEC Encoding IDs and FEC Instance IDs are subject to IANA Values of FEC Encoding IDs and FEC Instance IDs are subject to IANA
registration. For general guidelines on IANA considerations as they registration. For general guidelines on IANA considerations as they
apply to this document, see [2]. apply to this document, see [2].
This document assigns the Fully-Specified FEC Encoding ID 2 under the This document assigns the Fully-Specified FEC Encoding ID 2 under the
"ietf:rmt:fec:encoding" name-space to "Reed-Solomon Codes over "ietf:rmt:fec:encoding" name-space to "Reed-Solomon Codes over
GF(2^^m)". GF(2^^m)".
skipping to change at page 25, line 7 skipping to change at page 27, line 7
This document assigns the FEC Instance ID 0 scoped by the Under- This document assigns the FEC Instance ID 0 scoped by the Under-
Specified FEC Encoding ID 129 to "Reed-Solomon Codes over GF(2^^8)". Specified FEC Encoding ID 129 to "Reed-Solomon Codes over GF(2^^8)".
More specifically, under the "ietf:rmt:fec:encoding:instance" sub- More specifically, under the "ietf:rmt:fec:encoding:instance" sub-
name-space that is scoped by the "ietf:rmt:fec:encoding" called name-space that is scoped by the "ietf:rmt:fec:encoding" called
"Small Block Systematic FEC Codes", this document assigns FEC "Small Block Systematic FEC Codes", this document assigns FEC
Instance ID 0 to "Reed-Solomon Codes over GF(2^^8)". Instance ID 0 to "Reed-Solomon Codes over GF(2^^8)".
11. Acknowledgments 11. Acknowledgments
The authors want to thank Brian Adamson for his valuable comments. The authors want to thank Brian Adamson, Igor Slepchin, Stephen Kent,
The authors also want to thank Luigi Rizzo for comments on the and Francis Dupont for their valuable comments. The authors also
subject and for the design of the reference Reed-Solomon codec. want to thank Luigi Rizzo for his comments and for the design of the
reference Reed-Solomon codec.
12. References 12. References
12.1. Normative References 12.1. Normative References
[1] Bradner, S., "Key words for use in RFCs to Indicate Requirement [1] Bradner, S., "Key words for use in RFCs to Indicate Requirement
Levels", RFC 2119. Levels", RFC 2119.
[2] Watson, M., Luby, M., and L. Vicisano, "Forward Error [2] Watson, M., Luby, M., and L. Vicisano, "Forward Error
Correction (FEC) Building Block", Correction (FEC) Building Block", RFC 5052, August 2007.
draft-ietf-rmt-fec-bb-revised-07.txt (work in progress),
April 2007.
[3] Watson, M., "Basic Forward Error Correction (FEC) Schemes", [3] Watson, M., "Basic Forward Error Correction (FEC) Schemes",
draft-ietf-rmt-bb-fec-basic-schemes-revised-03.txt (work in draft-ietf-rmt-bb-fec-basic-schemes-revised-03.txt (work in
progress), February 2007. progress), February 2007.
12.2. Informative References
[4] Luby, M., Vicisano, L., Gemmell, J., Rizzo, L., Handley, M., [4] Luby, M., Vicisano, L., Gemmell, J., Rizzo, L., Handley, M.,
and J. Crowcroft, "The Use of Forward Error Correction (FEC) in and J. Crowcroft, "The Use of Forward Error Correction (FEC) in
Reliable Multicast", RFC 3453, December 2002. Reliable Multicast", RFC 3453, December 2002.
[5] "HMAC: Keyed-Hashing for Message Authentication", RFC 2104, [5] Rizzo, L., "Reed-Solomon FEC codec (revised version of July
February 1997.
[6] "Timed Efficient Stream Loss-Tolerant Authentication (TESLA):
Multicast Source Authentication Transform Introduction",
RFC 4082, June 2005.
12.2. Informative References
[7] Rizzo, L., "Reed-Solomon FEC codec (revised version of July
2nd, 1998), available at 2nd, 1998), available at
http://info.iet.unipi.it/~luigi/vdm98/vdm980702.tgz, and http://info.iet.unipi.it/~luigi/vdm98/vdm980702.tgz and
mirrored at http://planete-bcast.inrialpes.fr/", July 1998. mirrored at http://planete-bcast.inrialpes.fr/", July 1998.
[8] Mac Williams, F. and N. Sloane, "The Theory of Error Correcting [6] Mac Williams, F. and N. Sloane, "The Theory of Error Correcting
Codes", North Holland, 1977 . Codes", North Holland, 1977 .
[9] Luby, M., Shokrollahi, A., Watson, M., and T. Stockhammer, [7] Gohberg, I. and V. Olshevsky, "Fast algorithms with
"Raptor Forward Error Correction Scheme", preprocessing for matrix-vector multiplication problems",
draft-ietf-rmt-bb-fec-raptor-object-08 (work in progress), Journal of Complexity, pp. 411-427, vol. 10, 1994.
April 2007.
[10] Roca, V., Neumann, C., and D. Furodet, "Low Density Parity [8] Roca, V., Neumann, C., and D. Furodet, "Low Density Parity
Check (LDPC) Forward Error Correction", Check (LDPC) Forward Error Correction",
draft-ietf-rmt-bb-fec-ldpc-06.txt (work in progress), draft-ietf-rmt-bb-fec-ldpc-06.txt (work in progress),
May 2007. May 2007.
[11] Luby, M., Watson, M., and L. Vicisano, "Asynchronous Layered [9] Luby, M., Shokrollahi, A., Watson, M., and T. Stockhammer,
"Raptor Forward Error Correction Scheme",
draft-ietf-rmt-bb-fec-raptor-object-09 (work in progress),
June 2007.
[10] Luby, M., Watson, M., and L. Vicisano, "Asynchronous Layered
Coding (ALC) Protocol Instantiation", Coding (ALC) Protocol Instantiation",
draft-ietf-rmt-pi-alc-revised-04.txt (work in progress), draft-ietf-rmt-pi-alc-revised-04.txt (work in progress),
February 2007. February 2007.
[12] Adamson, B., Bormann, C., Handley, M., and J. Macker, [11] Adamson, B., Bormann, C., Handley, M., and J. Macker,
"Negative-acknowledgment (NACK)-Oriented Reliable Multicast "Negative-acknowledgment (NACK)-Oriented Reliable Multicast
(NORM) Protocol", draft-ietf-rmt-pi-norm-revised-04.txt (work (NORM) Protocol", draft-ietf-rmt-pi-norm-revised-05.txt (work
in progress), March 2007. in progress), March 2007.
[13] Paila, T., Walsh, R., Luby, M., Lehtonen, R., and V. Roca, [12] Paila, T., Walsh, R., Luby, M., Lehtonen, R., and V. Roca,
"FLUTE - File Delivery over Unidirectional Transport", "FLUTE - File Delivery over Unidirectional Transport",
draft-ietf-rmt-flute-revised-03.txt (work in progress), draft-ietf-rmt-flute-revised-04.txt (work in progress),
January 2007. October 2007.
[14] Gohberg, I. and V. Olshevsky, "Fast algorithms with [13] Jonsson, J. and B. Kaliski, "Public-Key Cryptography Standards
preprocessing for matrix-vector multiplication problems", (PKCS) #1: RSA Cryptography Specifications Version 2.1",
Journal of Complexity, pp. 411-427, vol. 10, 1994 . RFC 3447, February 2003.
[14] Kent, S., "IP Encapsulating Security Payload (ESP)", RFC 4303,
December 2005.
[15] "HMAC: Keyed-Hashing for Message Authentication", RFC 2104,
February 1997.
[16] "Timed Efficient Stream Loss-Tolerant Authentication (TESLA):
Multicast Source Authentication Transform Introduction",
RFC 4082, June 2005.
Authors' Addresses Authors' Addresses
Jerome Lacan Jerome Lacan
ENSICA/LAAS-CNRS ISAE
1, place Emile Blouin 1, place Emile Blouin
Toulouse 31056 Toulouse 31056
France France
Email: jerome.lacan@ensica.fr Email: jerome.lacan@isae.fr
URI: http://dmi.ensica.fr/auteur.php3?id_auteur=5 URI: http://dmi.ensica.fr/auteur.php3?id_auteur=5
Vincent Roca Vincent Roca
INRIA INRIA
655, av. de l'Europe 655, av. de l'Europe
Inovallee; Montbonnot Inovallee; Montbonnot
ST ISMIER cedex 38334 ST ISMIER cedex 38334
France France
Email: vincent.roca@inrialpes.fr Email: vincent.roca@inrialpes.fr
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